Abstract

A type of shearing interferometry is presented in which the wave front under test interferes with a radially reversed replica of itself. The radial reversal of the wave front can be achieved either by an axicon–lens system or by use of a circular grating. Experimental verification is shown.

© 1970 Optical Society of America

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References

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  1. W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967).
  2. J. H. McLeod, J. Opt. Soc. Am. 44, 592 (1954).
    [Crossref]
  3. J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

1958 (1)

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

1954 (1)

Dyson, J.

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

McLeod, J. H.

Steel, W. H.

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967).

J. Opt. Soc. Am. (1)

Proc. Roy. Soc. (London) (1)

J. Dyson, Proc. Roy. Soc. (London) A248, 93 (1958).

Other (1)

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967).

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Figures (6)

Fig. 1
Fig. 1

Formation of a reversed-radial-shearing interferogram: (a) wave front under test, (b) the wave front (solid curve) and a radially reversed copy (dashed curve), and (c) the phase difference Δ between the curves in (b) which is made visible in the reversed-radial-shear interferogram.

Fig. 2
Fig. 2

Radial reversal of a wave front by two axicons A1 and A2.

Fig. 3
Fig. 3

Optical arrangement of a reversed-radial-shearing interferometer using two axicons A1 and A2. The interferogram is displayed in plane I, which is an image of the object plane O. This figure shows how the point in O on the optical axis is imaged as a point in I by the lower path with a conventional optical system, and as a ring by the upper path that contains the axicons. Any other point of O is also imaged by the upper path as a point in I, the distance of which from the optical axis is reversed in relation to the distance of the point in O from the optical axis.

Fig. 4
Fig. 4

Interferograms of the phase object illustrated in Fig. 1. (a) is a conventional Mach–Zehnder-type interferogram of the object and (b) is the corresponding reversed-radial-shear interferogram.

Fig. 5
Fig. 5

Optical arrangement of a reversed-radial-shearing interferometer using a circular grating G.

Fig. 6
Fig. 6

Devices for obtaining a radial reversal of a wave front in a Michelson-type-interferometer arrangement.

Equations (3)

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I = 1 4 u ( r , φ ) + u ( r 0 - r , φ ) 2 .
I exp [ i ϕ ( r , φ ) ] + exp [ i ϕ ( r 0 - r , φ ) ] 2 = 4 cos 2 { [ ϕ ( r , ϕ ) - ϕ ( r 0 - r , φ ) ] / 2 } ,
Δ = ϕ ( r , φ ) - ϕ ( r 0 - r , φ ) = ( 2 p + 1 ) π ,